We don't like this concept because it's complicated and irrelevant. You can't walk up to a car at cruise night and calculate it's "effective gear ratio" unless you know its original tire size. Many people will say, "It's got 3.73:1 gears, but they act like 3.50s because the tires are taller." Taller than what? There is no standard from which to compare. Besides, "effective gear ratio" implies that a ratio has been changed, but tire size has no effect on axle ratio at all. Here's proof: If you have 4.10:1 gears, then the driveshaft will turn 4.1 times for each revolution of the tires regardless of their size.
However, changes in tire diameter do affect the car's cruise rpm, and perhaps its acceleration, because you've altered the number of tire revolutions per mile. For example, a tire with a true diameter of 26 inches has a circumference of 81.68 inches; a tire 30 inches tall has a circumference of 94.25 inches. That means each time the 30-inch tire completes one revolution it will move the car about 12 1/2 inches farther than the one revolution of the 26-inch tires. Therefore, the taller tire requires less input rpm (engine speed) to travel the same distance. Conversely, shorter tires require more engine speed per mph. That's why shorter tires seem to act like lower axle gears, and taller tires seem to act like higher gears.
There are two other reasons taller tires can tend to reduce acceleration. First, taller usually means bigger, which means heavier. Secondly, taller tires have a greater static loaded radius, or the distance from the center of the axleshaft to the ground when the tire is installed at operating pressure and loaded with the weight of the vehicle. The greater the static loaded radius, the greater the length of the lever between the axle and the ground, the greater the tire's ability to resist the acceleration of the car. However, taller tires also have a larger contact patch than shorter tires, so the dragstrip tractive advantages usually outweigh any disadvantages of taller tires, especially when the proper axle gears are chosen to compensate for the tire size.
The Formula You Need
Want to calculate your cruise rpm after a gear ratio or tire size swap? You'll need to know the following: the mph at which you want to calculate rpm, the transmission gear ratio, the rear axle ratio, and the true tire diameter. Plug them into the calculator like this:
|mph x trans ratio x axle ratio x336
Here's an example assuming 70 mph, a trans ratio of 1:1, 3.50:1 gears, and 30-inch-tall tires:
|70 x 1 x 3.50 x 336
When using this formula, keep two things in mind. First, that your true rpm will almost always be higher with an automatic trans without a lockup torque converter thanks to converter slippage. The exact percentage of real-world increase depends on the road speed, rpm, and type of converter, but figure at least a 10 percent increase. Also, never trust the sidewall designation or the manufacturer's specs when it comes to tire diameter. Get the tire, mount it on a rim, properly inflate it for your vehicle weight, and measure it yourself.